The Radioactive Nucleus as a Clock

If you have a gram of ⁹⁹Mo right now, then you know that after 66 hours, you are going to have a half gram of ⁹⁹Mo and a half gram of ⁹⁹Tc. This can be said without specifying the conditions under which you keep the sample, because you can't change it by heating it, by striking it with lightning, by combining it into a molecule, or any other environmental interaction short of a direct nuclear impact by a high speed particle.

The time for a given nucleus to decay is unpredictable and random, but the rate of decay of a sample is not random but dependent upon nuclear structure details through the decay constant. A sizable sample will have a significant fraction of Avogadro's number of nuclei, and the statistics of such a decay are such that it follows a precise exponential decay pattern. 某一核素的衰变时间是不可预测和随机的，但样品的衰变率并非随机，而是通过衰变常数依赖于核结构细节。一个数量可观的样品将包含阿伏伽德罗常数数量级的核素，此类衰变的统计特性使得其遵循精确的指数衰变模式。

The range of half-lives of heavy elements that emit alpha particles varies over 20 orders of magnitude, from about a tenth of a microsecond to 10 billion years. But they all follow exactly the same form of decay, an exponential decay determined by nuclear structure parameters. 重元素发射α粒子的半衰期范围跨度达20个数量级，从约十亿分之一秒到100亿年。但它们都遵循完全相同的衰变形式，即由核结构参数决定的指数衰变。

The natural radioactive series found on the Earth involve multiple steps, each step with its characteristic "parent" and "daughter" products. Because the radioactive half-life of a given radioisotope is not affected by temperature, physical or chemical state, or any other influence of the environment outside the nucleus save direct particle interactions with the nucleus, then radioactive samples continue to decay at a predictable rate. If determinations or reasonable estimates of the original composition of a radioactive sample can be made, then the amounts of the radioisotopes present can provide a measurement of the time elapsed.

One such method is called carbon dating, which is limited to the dating of organic (once living) materials. For longer time scales appropriate for geologic samples, the Rubidium-Strontium method is an example of a nuclear clock.

The longer-lived radioisotopes in minerals provide evidence of long time scales in geological processes. While original compositions cannot be determined with certainty, various combination measurements provide self-consistent values for the the times of formations of certain geologic deposits. These clocks-in-the-rocks methods provide data for modeling the formation of the Earth and solar system.